A continuity tester is very useful for checking printed-circuit boards. It indicates a sound connection by a squeak from a buzzer there is, therefore, no need to continually watch a meter.
The voltage across test terminals TP1 and TP2 is only 80 mV. That is not sufficient to test diodes, but it obviates the risk of damage to electronic components.
The design consists of a comparator IC-1, and an astable consisting of T1 and T2. whose frequency is around 1250 Hz for a supply voltage of 3 V. The astable is actuated the moment the output of IC-1 (pin 6) goes logic high. This happens when the resistance between TP1 and TP2 is low, so that the voltage at pin 2 of the comparator is lower than that at pin 3, which depends on the setting of P1. The circuit is powered by a 3-V battery (two 1.5 V cells in series), but may be maximum 12 V. At such a high supply voltage, it may be that the tone of the buzzer is too high: in that case, the values of C1 and C2 should be increased.
If a Type TLC271C is used instead of a TLC251 for IC-1, the supply voltage must be not lower than 3 V. At 3 V, the circuit draws a current of about 1.4 mA.